{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2025 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apache",
   "metadata": {},
   "source": [
    "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "you may not use this file except in compliance with the License.\n",
    "You may obtain a copy of the License at\n",
    "\n",
    "    http://www.apache.org/licenses/LICENSE-2.0\n",
    "\n",
    "Unless required by applicable law or agreed to in writing, software\n",
    "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "See the License for the specific language governing permissions and\n",
    "limitations under the License.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basename",
   "metadata": {},
   "source": [
    "# pandigital_numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "link",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/pandigital_numbers.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/main/examples/contrib/pandigital_numbers.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "doc",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "install",
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install ortools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "description",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "  Pandigital numbers in Google CP Solver.\n",
    "\n",
    "  From Albert H. Beiler 'Recreations in the Theory of Numbers',\n",
    "  quoted from http://www.worldofnumbers.com/ninedig1.htm\n",
    "  '''\n",
    "  Chapter VIII : Digits - and the magic of 9\n",
    "\n",
    "  The following curious table shows how to arrange the 9 digits so that\n",
    "  the product of 2 groups is equal to a number represented by the\n",
    "  remaining digits.\n",
    "\n",
    "     12 x 483 = 5796\n",
    "     42 x 138 = 5796\n",
    "     18 x 297 = 5346\n",
    "     27 x 198 = 5346\n",
    "     39 x 186 = 7254\n",
    "     48 x 159 = 7632\n",
    "     28 x 157 = 4396\n",
    "     4 x 1738 = 6952\n",
    "     4 x 1963 = 7852\n",
    "  '''\n",
    "\n",
    "  See also MathWorld http://mathworld.wolfram.com/PandigitalNumber.html\n",
    "  '''\n",
    "  A number is said to be pandigital if it contains each of the digits\n",
    "  from 0 to 9 (and whose leading digit must be nonzero). However,\n",
    "  'zeroless' pandigital quantities contain the digits 1 through 9.\n",
    "  Sometimes exclusivity is also required so that each digit is\n",
    "  restricted to appear exactly once.\n",
    "  '''\n",
    "\n",
    "  * Wikipedia http://en.wikipedia.org/wiki/Pandigital_number\n",
    "\n",
    "\n",
    "  Compare with the following models:\n",
    "  * MiniZinc: http://www.hakank.org/minizinc/pandigital_numbers.mzn\n",
    "  * Comet   : http://www.hakank.org/comet/pandigital_numbers.co\n",
    "  * ECLiPSe : http://www.hakank.org/eclipse/pandigital_numbers.ecl\n",
    "  * Gecode/R: http://www.hakank.org/gecoder/pandigital_numbers.rb\n",
    "  * ECLiPSe : http://hakank.org/eclipse/pandigital_numbers.ecl\n",
    "  * SICStus : http://hakank.org/sicstus/pandigital_numbers.pl\n",
    "\n",
    "  This model was created by Hakan Kjellerstrand (hakank@gmail.com)\n",
    "  Also see my other Google CP Solver models:\n",
    "  http://www.hakank.org/google_or_tools/\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "from ortools.constraint_solver import pywrapcp\n",
    "\n",
    "#\n",
    "# converts a number (s) <-> an array of integers (t) in the specific base.\n",
    "#\n",
    "\n",
    "\n",
    "def toNum(solver, t, s, base):\n",
    "  tlen = len(t)\n",
    "  solver.Add(\n",
    "      s == solver.Sum([(base**(tlen - i - 1)) * t[i] for i in range(tlen)]))\n",
    "\n",
    "\n",
    "def main(base=10, start=1, len1=1, len2=4):\n",
    "\n",
    "  # Create the solver.\n",
    "  solver = pywrapcp.Solver(\"Pandigital numbers\")\n",
    "\n",
    "  #\n",
    "  # data\n",
    "  #\n",
    "  max_d = base - 1\n",
    "  x_len = max_d + 1 - start\n",
    "  max_num = base**4 - 1\n",
    "\n",
    "  #\n",
    "  # declare variables\n",
    "  #\n",
    "  num1 = solver.IntVar(0, max_num, \"num1\")\n",
    "  num2 = solver.IntVar(0, max_num, \"num2\")\n",
    "  res = solver.IntVar(0, max_num, \"res\")\n",
    "\n",
    "  x = [solver.IntVar(start, max_d, \"x[%i]\" % i) for i in range(x_len)]\n",
    "\n",
    "  #\n",
    "  # constraints\n",
    "  #\n",
    "  solver.Add(solver.AllDifferent(x))\n",
    "\n",
    "  toNum(solver, [x[i] for i in range(len1)], num1, base)\n",
    "  toNum(solver, [x[i] for i in range(len1, len1 + len2)], num2, base)\n",
    "  toNum(solver, [x[i] for i in range(len1 + len2, x_len)], res, base)\n",
    "\n",
    "  solver.Add(num1 * num2 == res)\n",
    "\n",
    "  # no number must start with 0\n",
    "  solver.Add(x[0] > 0)\n",
    "  solver.Add(x[len1] > 0)\n",
    "  solver.Add(x[len1 + len2] > 0)\n",
    "\n",
    "  # symmetry breaking\n",
    "  solver.Add(num1 < num2)\n",
    "\n",
    "  #\n",
    "  # solution and search\n",
    "  #\n",
    "  solution = solver.Assignment()\n",
    "  solution.Add(x)\n",
    "  solution.Add(num1)\n",
    "  solution.Add(num2)\n",
    "  solution.Add(res)\n",
    "\n",
    "  db = solver.Phase(x, solver.INT_VAR_SIMPLE, solver.INT_VALUE_DEFAULT)\n",
    "\n",
    "  solver.NewSearch(db)\n",
    "  num_solutions = 0\n",
    "  solutions = []\n",
    "  while solver.NextSolution():\n",
    "    print_solution([x[i].Value() for i in range(x_len)], len1, len2, x_len)\n",
    "    num_solutions += 1\n",
    "\n",
    "  solver.EndSearch()\n",
    "\n",
    "  if 0 and num_solutions > 0:\n",
    "    print()\n",
    "    print(\"num_solutions:\", num_solutions)\n",
    "    print(\"failures:\", solver.Failures())\n",
    "    print(\"branches:\", solver.Branches())\n",
    "    print(\"WallTime:\", solver.WallTime())\n",
    "    print()\n",
    "\n",
    "\n",
    "def print_solution(x, len1, len2, x_len):\n",
    "  print(\"\".join([str(x[i]) for i in range(len1)]), \"*\", end=\" \")\n",
    "  print(\"\".join([str(x[i]) for i in range(len1, len1 + len2)]), \"=\", end=\" \")\n",
    "  print(\"\".join([str(x[i]) for i in range(len1 + len2, x_len)]))\n",
    "\n",
    "\n",
    "base = 10\n",
    "start = 1\n",
    "if len(sys.argv) > 1:\n",
    "  base = int(sys.argv[1])\n",
    "if len(sys.argv) > 2:\n",
    "  start = int(sys.argv[2])\n",
    "\n",
    "x_len = base - 1 + 1 - start\n",
    "for len1 in range(1 + (x_len)):\n",
    "  for len2 in range(1 + (x_len)):\n",
    "    if x_len > len1 + len2:\n",
    "      main(base, start, len1, len2)\n",
    "\n"
   ]
  }
 ],
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